The technical field of the invention is that of vibrating beam sensors, which use the sensitivity of the resonance frequency of a vibrating beam to a force exerted along its longitudinal axis, the mechanical phenomenon involved being similar to that which occurs, for example, when tuning a guitar string. The input quantity to be measured by the sensor is, for example, a force, a pressure or an acceleration.
The technical problem to be solved is that of avoiding degradation of the precision of measurement of a vibrating beam sensor when the sensor is subjected to severe conditions of a thermal environment.
The closest prior art brings together the following three approaches:
The first approach teaches the mounting of two vibrating beams in parallel but with axes that are substantially in opposite directions, then considering the difference in their frequencies of flexural vibration in order to eliminate the effect, on said frequencies, of the natural thermal expansion of the beams under the effect of the temperature.The second approach teaches the arrangement of an additional vibrating beam close to the sensor, which additional vibrating beam is to supply temperature information in frequency form, said information being intended to compensate, by a model, the effects of the temperature on the sensor.The third approach teaches operation of the sensor with, as the sensitive element, not one but two vibrating beams that form a tuning fork which is able to vibrate simultaneously in flexion mode at a first frequency and in torsion mode at a second frequency. Since each of the two frequencies is sensitive to the input quantity to be measured and to the temperature, after calibration of the device, observation of the two frequencies allows the input quantity and the temperature to be evaluated.
These teachings of the prior art are described in detail below in order to bring to light the disadvantages to which the invention offers a solution.
In order to illustrate the idea, the case of vibrating beam accelerometers (VBA) will be considered, which will be taken to describe these two approaches.
A vibrating beam accelerometer comprises a beam, one end of which is integral with a proof mass and the other end of which is integral with a fixed part, means for inducing flexural vibration of the beam, and an oscillating electronic loop which allows the flexural vibration of the beam to be maintained in resonance mode. The sensitive axis of the accelerometer refers to the direction in which an acceleration creates, by way of the proof mass, an axial force of extension or compression on the vibrating beam, which modifies its mechanical resonance frequency. The output quantity of the accelerometer is accordingly a frequency the variations of which are representative of the acceleration to be measured. The proof mass is generally connected to the fixed part by articulations which are to ensure that the proof mass resists acceleration directions other than the sensitive axis.
In order that the vibration of the beam has a good quality coefficient, and so that the measurement resolution of the accelerometer is satisfactory, the mechanical structure of the accelerometer is packaged in vacuo in a tight casing.
As with many sensors, temperature variations are a source of limitation of the performance of vibrating beam accelerometers. In the case of vibrating beam accelerometers, temperature variations cause variations in the frequency of the beam which can be wrongly interpreted as being caused by an acceleration.
The mechanisms of action of temperature are of different natures, depending on whether the temperature variation is slow or rapid.
A slow temperature variation is to be understood as meaning that the rate of variation of the temperature is sufficiently low that the temperature is virtually uniform throughout the structure of the accelerometer.
During a slow temperature variation, there are primarily only two phenomena that occur.
The first phenomenon is the natural modification of the dimensional and mechanical parameters of the beam, which intrinsically causes a variation in its resonance frequency. The material of which the beam is composed plays a decisive role, and it is known, for example, in the clock- and watch-making industry that quartz allows the influence of temperature on the resonance frequency of a flexurally vibrating beam to be reduced significantly.
The second phenomenon is present when the accelerometer is produced from a plurality of materials, for example when the accelerometer comprises a beam made of quartz that is attached to a proof mass and a fixed part that are made of metal. Because the coefficients of thermal expansion of those materials cannot strictly be equal, the differential expansion causes an axial force of extension or compression on the beam, which modifies its resonance frequency by the same mechanism as acceleration, that is to say, unfortunately, with the same effectiveness. For that reason, it is advantageous for the structure of the accelerometer to be produced from a single material. Accordingly, it is known, for example, to produce monolithic quartz accelerometer structures, which allows this second phenomenon to be eliminated and the influence of slow temperature variations thus to be limited to the first phenomenon, that is to say to the natural variations of the resonance frequency of the beam.
However, for applications which require a high precision of measurement, for example inertial navigation, the amplitudes of these natural variations in the frequency of the beam are still too great and cannot sufficiently be compensated by a model based on knowledge of the temperature obtained by means of a conventional temperature sensor positioned close to the accelerometer.
The first approach described below employs, to that end, two substantially identical accelerometer structures which are very close to one another, generally contained within the same tight casing, and operate in differential mode, that is to say are arranged so that their sensitive axes are in opposite directions, as is described in U.S. Pat. No. 5,962,786 in the name of the applicant. In that manner, the two structures “see” accelerations Γ and −Γ, respectively, of opposite directions and are subject, on the other hand, to virtually the same temperature variation (T−T0). Their respective frequencies F and F′ are written, in simplified form:F≈K0+K1·Γ+K2·Γ2+α1·(T−T0)+α2·(T−T0)2 F′≈K0+K1·(−Γ)+K2·(−Γ)2+α1·(T−T0)+α2·(T−T0)2 where, for each of the structures, K0 is the frequency in the absence of acceleration and at the reference temperature T0, K1 and K2 are the coefficients of sensitivity to the acceleration of first and second order, and α1 and α2 are the coefficients of sensitivity to the temperature of first and second order.
The output quantity S of such a differential accelerometer is the difference between the two frequencies F and F′:S≈F−F′≈2·K1·Γ
Accordingly, operation in differential mode on the one hand allows the response of the sensor to the acceleration to be linearised, and on the other hand allows the influence of the temperature almost to be eliminated. In practice, given the production imperfections, the sensitivity of the output S to the temperature is not zero but approximately two orders of magnitude smaller than that of each of the frequencies F and F′, which is generally sufficient.
There have just been explained, in the case of slow temperature variations, mechanisms of action of the temperature on the precision of the accelerometer, and ways of remedying them.
There will now be discussed the case of rapid temperature variations, on the basis of the differential accelerometer DA that is the subject-matter of the above-mentioned patent and shown in FIG. 1.
The disadvantage of this first approach is that it is not able to solve the problem of the degradation of the precision of measurement of the sensor when the sensor is subject to rapid temperature variations, as is shown in the following.
Said differential accelerometer DA is composed of two monolithic quartz accelerometer structures TAe1 and TAe2 which are substantially identical. Each accelerometer structure has the general form of a disk and its sensitive axis is approximately perpendicular to the plane of the disk, the sensitive axes of the two structures being in opposite directions. In general, the diameter of the disk is less than 10 mm and its thickness is less than 1 mm. For each structure, the vibrating beam (3e1; 3e2) is integral at one end with a first solid part (2e1; 2e2) serving as the proof mass and at the other end with a second solid part (4e1; 4e2) serving as the fixed part with respect to the operation of the structure subjected to an acceleration. In general, the cross-sectional dimensions of the vibrating beam are less than 100 μm. Each of said solid parts is generally U-shaped. The frame (5e1; 5e2) surrounding the two solid parts is intended to preserve the quality of the flexural vibration of the beam but plays virtually no role with respect to the operation of the structure subjected to an acceleration.
This differential accelerometer known from the prior art belongs to the category of the electromechanical microsystems (MEMS) and has good performances as long as the temperature variations are relatively slow. For relatively rapid variations, on the other hand, for example 10° C./min, the precision of the accelerometer is substantially degraded. This is due mainly to the fact that a rapid temperature variation generally induces on the one hand a spatial temperature gradient inside the tight casing, more precisely a temperature difference between the two vibrating beams, and on the other hand a spatial temperature gradient within each accelerometer structure, as will be explained hereinbelow with reference to FIG. 2.
FIG. 2 shows a partial view of one of the two structures (TAe1) of the accelerometer DA of FIG. 1, limited principally to the vibrating beam 3e1, to the solid parts 2e1 and 4e1, and to the articulations 81 and 82. It will be noted, as explained in the above-mentioned patent, that the structure can be produced in a single chemical machining step by simultaneously etching the two faces of a quartz wafer to a depth corresponding to the thickness c of the beam and of the articulations. This simplicity of production allows a low manufacturing cost to be obtained, all the more so since a plurality of structures can be machined simultaneously in a single wafer, for example about twenty structures in a wafer having surface dimensions of 38.1 mm×38.1 mm.
The flexural vibration of the beam takes place parallel to the plane of the structure, as is shown in an exaggeratedly enlarged manner by the dotted line in FIG. 2. This enables the frequency of vibration to have a relatively low dispersion over a production group, because the frequency of the flexural vibration of the beam depends greatly on its length (L3) and on its cross-sectional dimension taken in the vibration plane, in the present case its width l, those two dimensions being obtained by very precise photolithographic processes, while its other cross-sectional dimension, in the present case its thickness c obtained by stopping chemical machining, is less easy to control.
When the structure is subject to a temperature variation, the conduction of heat by the solid part 4e1 to the solid part 2e1 takes place solely through the vibrating beam and the articulations, that is to say through the thin portions, which behave like a brake with respect to the conduction of heat. Under such conditions, it is known that the temperature of each of the solid parts is substantially uniform and that the difference ΔT between the temperatures of the two solid parts is proportional to the rate of temperature variation.
For each of the thin portions, of parallelepipedal shape, the conventional equations of heat conduction show that the temperature varies substantially linearly between its ends integral with the solid parts. The vibrating beam 3e1 and the articulations 81 and 82 therefore have the same mean temperature T, T being the temperature at the middle of their length. Accordingly, the temperature of the vibrating beam and of the articulations varies linearly between T−ΔT/2 and T+ΔT/2.
The length of the articulations 81 and 82 will be called L8, and it will be noted that the position of the articulations is in line with the middle of the length L3 of the vibrating beam. Under those conditions, the length dimension of each of the parallel limbs of the U-shaped solid parts 2e1 and 4e1 is (L3-L8)/2.
With the aid of a one-dimensional model parallel to the longitudinal axis of the vibrating beam, it is now possible to express the impact of the spatial temperature gradient on the expansions of the two paths of material joining each of the two ends of the vibrating beam, the first path passing through said beam and the second path passing through the articulations. With “a” denoting the coefficient of thermal expansion of the material:
Expansion of the First Path:a·T·L3Expansion of the Second Path:a·(T−ΔT/2)·(L3−L8)/2+a·T·L8+a·(T+Δ/2)(L3−L8)/2=a·T·L3
After simplification in the second equation it will be seen that the expansions of the two paths are theoretically identical and that no axial force of expansion or compression is thus theoretically exerted on the vibrating beam. That would not be the case if the articulations were not situated in line with the middle of the length L3 of the vibrating beam, because the expansions of the two paths of material would not be balanced and there would result an axial force of extension or compression responsible for a variation in the frequency of the vibrating beam, said frequency variation being proportional to ΔT and therefore proportional to the rate of temperature variation δT/δt.
In practice, it is difficult to obtain this balance, which makes high demands on production tolerances. Accordingly, each of the two structures constituting the differential accelerometer has a sensitivity to δT/δt. When the two structures are produced in the same batch, typically by collective chemical machining from a single quartz wafer, the sensitivities to δT/δt can be relatively similar, which would lead to the hope of a reduction in the sensitivity of the differential output S. In reality, that reduction can be obtained only if the two vibrating beams “see” precisely the same rate of temperature variation δT/δt, which is generally not the case. Accordingly, the frequencies F and F′ delivered by the two structures are written, in simplified form:F≈K0+K1·Γ+K2·Γ2+α1·(T−T0)+α2·(T−T0)2+λ·δT/δt F′≈K0+K1·(−Γ)+K2·(−Γ)2+α1·(T′−T0)+α2·(T′−T0)2+λ′·δT/δt where T and T′ are the mean temperatures of the two vibrating beams, and λ and λ′ are the coefficients of sensitivity of the two frequencies to the rate of temperature variation.
The reader will have noted that, in the presence of rapid temperature variations, the frequency of each of the vibrating beams is associated with the temperature by two very different phenomena: the first involves the instantaneous mean temperature of the beam and is related to the phenomenon of the natural modification of the dimensional and mechanical parameters of the beam in the case explained above of slow temperature variations, and the second phenomenon involves the rate of temperature variation which induces an axial force of extension or compression on the beam. In addition, the mean temperatures of the two beams are not identical, like their rates of variation.
Under those conditions, it is difficult in practice to take advantage of operation in differential mode, unless a sufficiently high-performance casing were produced and assemblies of the two structures in the casing sufficiently identical to obtain, with sufficient identity, T≈T′ and δT/δt≈δT′/δt were produced. However, such a casing and such assemblies would lead to an excessive production cost in comparison with the low cost of producing structures made of quartz.
The second approach is described in the article entitled “Precision gravity measurement utilizing Accelerex vibrating beam accelerometer technology” by Brian L. Norling (IEEE PLANS 1990), in which there is shown an additional vibrating element (a flexurally vibrating quartz beam), integral with the inside wall of the tight casing, and which is intended solely to provide temperature information in frequency form. Said temperature information is used to compensate, by a model, the effects of the temperature on the output signal, which is also frequential, of the vibrating beam accelerometer.
This compensation is very effective for very slow temperature variations, as is indicated in the article, which recommends protecting the accelerometer from transient temperature states.
The disadvantage of this second approach is that, as for the first approach, it does not allow the problem presented by rapid temperature variations to be solved. In the case of the second approach, the rapid temperature variations induce a relatively great spatial temperature gradient inside the tight casing, and in particular a temperature difference between the additional vibrating element and the vibrating beam of the accelerometer structure. Accordingly, the temperature indication provided by the additional vibrating element is not sufficiently representative of the temperature of the vibrating beam of the accelerometer structure.
The third approach is described in the article entitled “Dual-mode temperature compensation for a comb-driven MEMS resonant strain gauge” by Robert G. Azevedo (Sensors and Actuators A: Physical 2008), in which there is shown a sensitive sensor element, said sensitive element comprising a single resonator composed of a tuning fork having two substantially identical beams (double-ended tuning fork, DETF). The tuning fork can be seen as replacing the single beam 3e1 of the first approach illustrated in FIG. 2.
Said sensitive element further comprises two substantially identical solid parts, which are of a size larger than that of the tuning fork and are arranged on either side of the tuning fork. Each solid part is fixed to a beam by a flexible portion in the vicinity of the middle of the length of the beam, and its role is that of a comb-drive actuator, permitting high effectiveness of the actuation.
The device is capable of vibrating according to two particular modes. For the first particular mode, the two beams vibrate torsionally in antiphase relative to one another (mode A at 86.1 KHz) and for the second particular mode, the two beams vibrate flexurally in antiphase relative to one another (mode D at 218 KHz). For each of the two modes, the two solid parts mainly play an inertia role (rotational inertia for the first mode and translational inertia for the second mode). Accordingly, the zone of fixing of each solid part to the vibrating beam corresponds to a vibration antinode, more precisely a torsional vibration antinode for the first mode and a flexural vibration antinode for the second mode.
The two modes are each sensitive to the input quantity to be measured (for example a force or an acceleration) and to the temperature, the important fact being that the coefficients of those sensitivities are not in the same ratio for the two modes, which, by observing the variations of their frequencies, allows the input quantity and the temperature to be discerned, for example by solving a system of two equations with two unknowns.
This third approach is very effective for very slow temperature variations.
The disadvantage of this third approach is that, as for the first and second approaches, it does not allow the problem presented by rapid temperature variations to be solved. In the case of the third approach, the two modes, when subjected to a rapid temperature variation, would see their frequencies vary as a function of three parameters: the input quantity to be measured, the temperature T, and the rate of temperature variation δT/δt, as explained above for the first approach. It would therefore not be possible, by observing the variations in the frequencies of the two modes, to discern those three parameters, since this would be equivalent to wishing to solve a system of two equations with three unknowns.
It may nevertheless be interesting to take inspiration from this third approach and try to involve another mode of vibration of the device that is not sensitive to the axial forces of extension or compression applied to the tuning fork. Accordingly, this other mode of vibration would not be sensitive either to the input quantity to be measured or to the rate of temperature variation δT/δt as explained above, but would be sensitive only to the temperature T. It would then be possible, by measuring the frequency of that other mode of vibration, to know T and, by means of two successive measurements of said frequency, to determine a “discrete partial derivative” almost equal to δT/δt. Knowledge of those two parameters, associated with the measurement of the frequency, for example, of mode D, which depends on the input quantity, on T and on δT/δt, would allow the input quantity to be determined.
Unfortunately, the configuration of the device according to the third approach does not permit the existence of such another mode of vibration, as is possible to understand from the article in view of the illustrations showing eight modes of vibration of the device. The dissymmetry created by the fixing of each solid part on one side of the beam is responsible for the fact that the zone of said fixing is a translational or rotational antinode of the beam, whatever the mode of vibration of the device. Accordingly, the frequency of the mode of vibration is sensitive to the axial forces of extension or compression applied to the tuning fork, that is to say sensitive to the input quantity to be measured and to δT/δt.